This invention pertains to analog-to-digital converters (ADCs) and digital-to-analog converters (DACs), and has particular reference to digital filters which decimate the output of a sigma-delta ADC and to digital filters which interpolate the input to a sigma-delta DAC.
An analog signal may be converted to single-bit stream by means of a sigma-delta converter. This conversion generally takes place at very high frequencies (perhaps 8 megahertz), to avoid aliasing, even through the signal of interest to a downstream digital signal processor is at a much lower frequency (perhaps only 122 hertz). The bit stream must then be decimated, so as to gain precision in amplitude at the expense of frequency (which is tolerable, since the Nyquist frequency is also much lower than the sampling frequency), but such decimation must be done without itself introducing aliasing. Digital filters which do this are complex and expensive.
Likewise, a precise digital signal produced at a low frequency from a digital signal processor must be converted to a very high frequency single-bit stream before it may be converted to an analog signal by a sigma-delta converter. This requires that values be interpolated between the sparse Nyquist sampling points, again without introducing aliasing. Digital filters which do this are also complex and expensive.